mathsurgery - Mental calculations and checking

All
• Extend mental methods for whole-number calculations, for example to multiply a two-digit by a one-digit number (e.g. 12 × 9), to multiply by 25 (e.g. 16 × 25), to subtract one near multiple of 1000 from another (e.g. 6070 – 4097) (Y5)
• Use knowledge of place value and multiplication facts to 10 × 10 to derive related multiplication and division facts involving decimals (e.g. 0.8 × 7, 4.8 ÷ 6) (Y6)
• Calculate mentally with integers and decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U (Y6)
• Use approximations, inverse operations and tests of divisibility to estimate and check results (Y6)

Most
• Understand the significance of a counter-example
• Calculate accurately, selecting mental methods or calculating devices as appropriate
• Understand and use the rules of arithmetic and inverse operations in the context of positive integers and decimals
• Use the order of operations, including brackets
• Strengthen and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings; solve simple problems mentally
• Recall number facts, including positive integer complements to 100 and multiplication facts to 10 × 10, and quickly derive associated division facts
• Check results by considering whether they are of the right order of magnitude and by working problems backwards

Some
• Identify exceptional cases or counter-examples
• Understand and use the rules of arithmetic and inverse operations in the context of integers and fractions
• Use the order of operations, including brackets, with more complex calculations
• Strengthen and extend mental methods of calculation, working with decimals, fractions, percentages, squares and square roots, and cubes and cube roots; solve problems mentally
• Recall equivalent fractions, decimals and percentages; use known facts to derive unknown facts, including products involving numbers such as 0.7 and 6, and 0.03 and 8
• Make and justify estimates and approximations of calculations
• Select from a range of checking methods, including estimating in context and using inverse operations

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Mental calculations and checking